Tunneling Qubit Operation on a Protected Josephson Junction Array

We discuss a protected quantum computation process based on a hexagon Josephson junction array. Qubits are encoded in the punctured array, which is topologically protected. The degeneracy is related to the number of holes. The topological degeneracy is lightly shifted by tuning the flux through specific hexagons. We also show how to perform single qubit operation and basic quantum gate operations in this system.Comment: 8 pages, 4 figures. The published version in Phys. Rev., A81(2010)01232

A variation of a classical Turán-type extremal problem

AbstractA variation of a classical Turán-type extremal problem (Erdős on Graphs: His Legacy of Unsolved Problems (1998) p. 36) is considered as follows: determine the smallest even integer σ(Kr,s,n) such that every n-term graphic non-increasing sequence π=(d1,d2,…,dn) with term sum σ(π)=d1+d2+⋯+dn≥σ(Kr,s,n) has a realization G containing Kr,s as a subgraph, where Kr,s is a r×s complete bipartite graph. In this paper, we determine σ(Kr,s,n) exactly for every fixed s≥r≥3 when n≥n0(r,s), where m=[(r+s+1)24] andn0(r,s)=m+3s2−2s−6,ifs≤2randsis even,m+3s2+2s−8,ifs≤2randsis odd,m+2s2+(2r−6)s+4r−8,ifs≥2r+1

Deletion of the V2 vasopressin receptor gene in two Chinese patients with nephrogenic diabetes insipidus

BACKGROUND: Congenital nephrogenic diabetes insipidus (NDI) is a rare X-linked inherited disorder characterized by the excretion of large volumes of diluted urine and caused by mutations in arginine vasopressin receptor 2 (AVPR2) gene. To investigate the mutation of AVPR2 gene in a Chinese family with congenital NDI, we screened AVPR2 gene in two NDI patients and eight family members by PCR amplification and direct sequencing. RESULTS: Five specific fragments, covering entire coding sequence and their flanking intronic sequences of AVPR2 gene, were not observed in both patients, while those fragments were all detected in the control subjects. Several different fragments around the AVPR2 locus were amplified step by step. It was revealed that a genomic fragment of 5,995-bp, which contained the entire AVPR2 gene and the last exon (exon 22) of the C1 gene, was deleted and a 3-bp (GAG) was inserted. Examination of the other family members showed that the mothers and the grandmother were carriers for this deletion. CONCLUSION: Our findings suggest that the two patients in a Chinese family suffering from congenital NDI had a 5,995-bp deletion and 3-bp (GAG) insertion at Xq28. The deletion contained the entire AVPR2 gene and exon 22 of the C1 gene

Quantum correlations in a cluster-like system

We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations. All these facts show that the system is topologically ordered. We also find a string order parameter to characterize the quantum phase transition. Besides, we investigate two-site correlations including entanglement, quantum discord and mutual information. We study the different divergency behaviour of the correlations. The quantum correlation decays exponentially in both topological and magnetic phases, and diverges in reversed power law at the critical point. And we find that in TQPT systems, the global difference of topology induced by dimension can be reflected in local quantum correlations.Comment: 7 pages, 6 figure